Phase Portraits of Control Dynamical Systems

1. Introduction.- 2. Controllable Dynamical System (CDS.- 3. Differential Inclusion. Equivalence Classes of CDS.- 4. Transformation of CDS to Phase Velocity Unit Vectors.- 5. Indicatrix of CDS.- 6. Degree of Freedom in Control of CDS.- 7. The Hamiltonian of CDS as a Support function.- 8. Types of Cones of Admissible Direction of CDS.- 9. Domain of Free Trajectories of CDS.- 10. The Principle of Inclusion in the Event Space.- 11. The Boundary of an Integral Funnels of a Differential Inclusion.- 12. Relationship of the Boundary of an Integral Funnel with the Hamiltonian-Jacobi Equation.- 13. The Principle of Inclusion for an Autonomous CDS in the State Space Integration of CDS.- 14. Boundary of the Trajectory Funnel of CDS.- 15. Geometrical Construction of the Boundary of Trajectory Funnel.- 16. The Euler-Lagrange Equation for the Boundary of Trajectory Funnel.- 17. Hatched Boundaries of Trajectory Funnels Manifold of Reverse Hatching (MRH.- 18. Singular Manifolds of CDS in State Space.- 19. Invariant Manifold of CDS.- 20. Singular and Invariant Manifolds of Linear CDS.- 21. Domain of Free Trajectories on Invariant Manifolds.- 22. Trajectories Funnel on Invariant Manifolds.- 23. Separating Hypersurfaces in State Spaces.- 24. Admissible Manifolds of CDS in State Space.- 25. Phase Portrait of CDS.- 26. Transient and Relative Motion of CDS.- 27. CDS with Ellipsoidal Indicatrix.- 28. CDS and Continuous Non Linear Media. The Principle of Maximum of Flows of Substance. Laplace Operator of CDS.- 29. CDS and Finsler Metric.- 30. Optical Analogue of CDS.- 31. Correspondence between CDSs and Mechanical Systems.- 32. CDS Subject to Phase Constraints.- 33. Singular Sets of Two-Dimensional CDSs.- 34. Phase Portrait of CDS on Two-Dimensional Manifolds.- 35. Examples on Construction ofPhase Portrait of Two-Dimensional CDS.- 36. Phase Portrait of Two-Level Quantum-Mechanical CDS.- 37. Example of Decomposable Bilinear CDS in Three-Dimensional Space.- 38. Controllability of General Bilinear CDS on Plane.- 39. Trajectory Funnel in Backward Time.- 40. Optimal Control.